What you're describing sounds similar to how I felt after my very first cruise. I got off the ship, and for about a week, it seemed like the room was "moving" ever so slightly. It felt like everything was slowly rocking back and forth. When I tried to walk, it felt as if I was walking against some very strong wind, while someone was nudging me from behind. It's a weird feeling. It did go away, but it took about a week.
The weird thing about it was while I was on the ship, I felt just fine. The dizziness or rocking sensation didn't really kick in until after the cruise.
I'm no expert, but I'm guessing there's something hypnotic about not always being able to see the direction you are traveling when you feel motion, and so the mind tries to fill in the missing pieces and gets it wrong, throwing things out of synch just a little. If you've ever taken a long road trip, and fallen asleep in the car while it was moving, it's easy to get the sensation that the car is traveling backwards instead of forward. It's funny how the mind can do that.
I doubt what you're describing is serious, but if you are concerned, you could consult a doctor or an "ask a nurse" hot line and get a professional opinion. Chances are, you will be just fine after a day or so and the problem will go away on its own.